ABSTRACT
A matrix is a tool for arranging numerical values and/or functions in an organized manner. One of the simplest operations that can be performed on a matrix is multiplication by a scalar. A scalar is a quantity that can be characterized by a single value at every point in space. A scalar can be a function of position, but it does not have direction associated with it. The identity matrix is a square matrix whose elements are one in the diagonal positions and zero everywhere else. The components of the identity matrix can be written succinctly using the Kronecker delta symbol. The calculus is the fundamental mathematical tool that has allowed numerical techniques such as the finite element method to come into being. A key mathematical concept behind modern nonlinear finite element procedures is the R. L. Taylor series expansion.
